Connecting pairwise and positional election outcomes

Another perspective on Borda’s paradox

“…We extend the results of Saari and McIntee (2013) in order to answer questions about the required conditions for a profile 1 to never exhibit either the strong or the strict Borda paradoxes under all weighted scoring rules and any given number of voters in threecandidate elections. The new technique developed in Saari and McIntee (2013) identifies all profiles that satisfy any specified pairwise and weighted criteria, such as where Condorcet winner is ranked first by any weighted scoring rule.…”

“…The new technique developed in Saari and McIntee (2013) identifies all profiles that satisfy any specified pairwise and weighted criteria, such as where Condorcet winner is ranked first by any weighted scoring rule. More exactly, all the conclusions are extracted from the differences of votes between candidates in pairwise majority elections.…”

“…Similarly to Saari and McIntee (2013), we will use a technical assumption, which is needed to separate the different cases of our results. This condition is defined as follows:…”

“…For a detailed description of Saari's voting geometry, the reader is referred to Saari (1989Saari ( , 1995Saari ( , 2010. 3 We particularly use the new way to analyze three-candidate relationships among pairwise and positional election outcomes that is developed in Saari and McIntee (2013). In the following, we present an overview of this methodology, and full details about this procedure are given in the original paper.…”

Monotonicity-based consensus states for the monometric rationalisation of ranking rules with application in decision making

“…Connecting both positional and pairwise election outcomes is a relevant topic in social choice theory [145]. As a result of Theorem 5.3, we know that all ranking rules belonging to the most prominent family of ranking rules based on positional information -scoring ranking rules -lead to the same outcome in case the scorix is monotone.…”